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 Citrix 2005-01-27 03:52

Sierpinski base 4

I have a slow computer that won't be of much help to the PSP project, so I am working on this problem on that computer. If anyone has any computers that won't be of much help to PSP can consider to help with this

66741 is the smallest number (k) that is a multiple of 3 and k*4^n+1 is never prime!

THe following k and n are left: (20), Please eliminate. Use Newpgen and LLR 3.5. Remember to enter base 4 than 2.
Post below to reserve a k. The aim is to take all the k's to 100,000 and then stop.

Scores
Mark 3
Footmaster 3
Citrix 0
Jean Penne 1
Mystwalker 1
masser 1

k Upper limit Relative weight Reserved by
5886 10000 92 Citrix
8139 10000 86 Citrix
18534 50000 80 Citrix
23451 46000 332 Mystwalker
23799 10000 268
33771 10000 142 Jean Penne
33879 20000 716 Mystwalker
34914 10000 455
35874 10000 448
41709 10000 410 Geoff
42717 10000 622 Geoff
49386 10000 319
51171 10000 731 masser
53226 10000 177 Carlos
55611 20000 536
60849 10000 387
60891 10000 275
63411 10000 316
64494 10000 272 Keller
66741 Sierpinski number for base 4

9 primes found so far!
15441*2^20584+1 is prime! Time: 1.172 sec. by Footmaster
21069*2^23006+1 is prime! Time: 1.751 sec. by Footmaster
21699*2^72874+1 is prime! Time: 21.318 sec. by Footmaster
14661*2^91368+1 is prime! Time: 42.331 sec. by Jean Penne
58791*2^79420+1 is prime! Time: 27.092 sec. by Mystwalker
52839*2^32558+1 is prime! Time: 2.640 sec. by masser
50166*4^12490+1 is prime! by Mark
45306*4^14484+1 is prime! by Mark
30579*4^24297+1 is prime! by Mark

Have fun eliminating these! :bounce:

 Jean Penné 2005-01-27 14:52

How did you choose the candidate k values ?

k values :

let N = k*4^n +1 with k odd.

I wish to compute N modulo 3.

4 = 1 (mod 3), so 4^n = 1 (mod 3)

so, N = k+1 (mod 3) All the possibilities are here :

k = 0 (mod 3) ==> N = 1 (mod 3)
k = 1 (mod 3) ==> N = 2 (mod 3)
k = 2 (mod 3) ==> N = 0 (mod 3), so these k's are all Sierpinski base 4 !!

Without any restriction on the k values, the "Sierpinski base 4" problem
would be rather trivial, because the least Sierpinki would be k = 5!

( I verified that with Newpgen...)

So, I understand why you added the condition 3 | k in your definition...
But why do you also exclude k = 1 (mod 3) ? Perhaps to avoid the values
already taken by Seventeen or Bust project, am I wrong ?

Regards,
Jean

 Citrix 2005-01-29 16:52

Here is the updated tables so far!

Open:
k Upper limit Relative weight
49386 10000 319
60849 10000 387
63411 10000 316
42717 100000 622

Reservations:
5886 Citrix
8139 Citrix
18534 Citrix
23451 Mystwalker (on hold...see message 46 for newpgen files)
33771 Jean Penne
33879 Mystwalker (on hold...see message 46 for newpgen files)
51171 masser
64494 Keller

Primes:
15441*4^10292+1 is prime! Footmaster
21069*4^11503+1 is prime! Footmaster
21699*4^36437+1 is prime! Footmaster
14661*4^45684+1 is prime! Jean Penne
58791*4^39710+1 is prime! Mystwalker
52839*4^16279+1 is prime! masser
50166*4^12490+1 is prime! Mark
45306*4^14484+1 is prime! Mark
30579*4^24297+1 is prime! Mark
53226*4^44874+1 is prime! em99010pepe
41709*4^40297+1 is prime! geoff
60891*2^40144+1 is prime! Jean Penne
55611*4^20106+1 is prime! Citrix
23799*4^52945+1 is prime! Ken_g6

Scores:
em99010pepe 1
Footmaster 3
Jean Penne 2
Mark 3
masser 1
Mystwalker 1
Geoff 1
Ken_g6 1
Citrix 1

12 k's left

 Jean Penné 2005-01-29 19:10

Still another one!

33771*4^89100+1 = 33771*2^178200+1 is prime! Time: 183.245 sec.

I think we enter now in the top 5000 !

I wish to reserve k = 42717 and continue it...

 Citrix 2005-01-31 16:57

k Upper limit Relative weight Reserved by
5886 50000 92 Citrix
8139 10000 86 Citrix
18534 50000 80 Citrix
33879 30000 716 Mystwalker
42717 100000 622 Jean Penne
49386 10000 319 Footmaster
60849 10000 387 masser
63411 10000 316 Footmaster
23451 60000 332 Mystwalker
64494 10000 272 Keller
66741 Sierpinski number for base 4

10 k's left

Top 5000 primes
33771*2^178200+1 is prime! Time: 183.245 sec.
51171*2^184528+1 is prime! Time: 87.521 sec.

 Footmaster 2005-01-31 17:05

63411*2^72064+1 is prime! Time: 42.157 sec.

 Citrix 2005-02-01 00:16

k Upper limit Relative weight Reserved by
5886 50000 92 Citrix
8139 10000 86 Citrix
18534 50000 80 Citrix
33879 30000 716 Mystwalker
42717 100000 622 Jean Penne
49386 10000 319 Footmaster
60849 10000 387 masser
23451 60000 332 Mystwalker
64494 10000 272 Keller
66741 Sierpinski number for base 4

9 k's left

Top 5000 primes
33771*2^178200+1 is prime! Time: 183.245 sec.
51171*2^184528+1 is prime! Time: 87.521 sec.

 Citrix 2005-02-01 05:08

8139*4^12977+1 is prime!

k Upper limit Relative weight Reserved by
5886 50000 92 Citrix
18534 57750 80 Citrix
33879 30000 716 Mystwalker
42717 100000 622 Jean Penne
49386 10000 319 Footmaster
60849 10000 387 masser
23451 60000 332 Mystwalker
64494 10000 272 Keller
66741 Sierpinski number for base 4

8 k's left

Top 5000 primes
33771*2^178200+1 is prime! Time: 183.245 sec.
51171*2^184528+1 is prime! Time: 87.521 sec.

 Footmaster 2005-05-25 06:44

49386*2^357416+1 is Prime!

I'll like to take 60849 next.

See if I get lucky with this one.

Regards

Foots

PS. When I submitted it it at prime pages it said this:
"The description "49386*2^357416+1" was modified to "24693*2^357417+1" in accordance with our canonicalization procedures. "

 Footmaster 2005-06-20 10:21

33879*2^378022+1 is prime!

only 5 left now :smile:

 Jean Penné 2005-11-05 16:11

k = 42717 is over !

Going back from a trip in Viet Nam and Cambodia, I found this on my P4 :

42717*2^905792+1 is prime! Time: 7292.117 sec.

So, now, only 4 k's remain to be eliminated !

This is very encouraging, so, I wish now to take k = 23451

Happy hunting to all,

Jean

 Jean Penné 2005-12-20 21:19

The project has found 24 Primes / 28 !

Thank you, Citrix!
I submitted the last prime found.

Also, I registered all the primes found by this project, sorted by dates :

15441*2^20584+1 is prime! Time: 1.172 sec. by Footmaster 27/01/05, 03:17PM
21069*2^23006+1 is prime! Time: 1.751 sec. by Footmaster 27/01/05, 03:51PM
21699*2^72874+1 is prime! Time: 21.318 sec. by Footmaster 27/01/05, 06:43PM
14661*2^91368+1 is prime! Time: 42.331 sec. by Jean Penné 27/01/05, 10:03PM
52839*2^32558+1 is prime! Time: 2.640 sec. by masser 27/01/05, 11:19PM
58791*2^79420+1 is prime! Time: 27.092 sec. by Mystwalker 27/01/05, 11:21PM
45306*2^28968+1 is prime! by Mark 27/01/05, 11:29PM
50166*2^24980+1 is prime! by Mark 27/01/05, 11:29PM
35874*2^53926+1 is prime! (121.4506s+0.0058s) by tcadigan 28/01/05, 06:41AM
34914*2^29562+1 is prime! (31.6149s+0.0012s) by tcadigan 28/01/05, 07:13AM
53226*2^89748+1 is prime! Time: 33.184 sec.by em99010pepe 28/01/05, 09:30AM
30579*2^48594+1 is prime! by Mark 28/01/05, 12:02AM
41709*2^80594+1 is prime! by geoff 29/01/05, 05:38AM
60891*2^40144+1 is prime! Time: 6.498 sec. by Jean Penné 29/01/05, 09:30AM
23799*2^105890+1 = 23799*4^52945+1 is prime! by Ken_g6 29/01/05, 05:45PM
55611*2^40212+1 is prime! by Citrix 29/01/05, 05:46PM
33771*2^178200+1 is prime! Time: 183.245 sec. Jean Penné 29/01/05, 08:10PM
51171*2^93736+1 is prime! Time: 19.943 sec. by masser 31/01/05, 04:18PM
51171*2^184528+1 is prime! Time: 87.521 sec. by masser <<
63411*2^72064+1 is prime! Time: 42.157 sec.by Footmaster 31/01/05, 06:05PM
8139*2^25954+1 is prime! by Citrix 01/02/05, 06:08AM
5886*2^108040+1 is prime! Time: 76.371 sec. by Jean Penné 06/02/05, 09:28AM
49386*2^357416+1 is Prime! by Footmaster 25/05/05, 08:44AM
33879*2^378022+1 is prime! by Footmaster 20/06/05, 12:21PM
42717*2^905792+1 is prime! Time: 7292.117 sec.Jean Penné 14/10/05, 08:18PM

My new k is at 925952 base 2.

Merry Christmas and Best Regards,
Jean

New DB id is 835, the id should be converted into a project in 2-3 days.

MY k is at 850000.[/QUOTE]

1 Attachment(s)
[QUOTE=Citrix]Could I have the latest sieve file?[/QUOTE]

here it is. I haven't updated Jean and my status, haven't seen the need, but also haven't been sieving recently.

 Jean Penné 2006-04-03 20:05

k=23451 tested up to n=1250044

Hi,

I reached this evening n=1250044 base 2, no prime found... so, continuing...
The bad new is that FFT length has just increased to 128K and so, the time for each test increased from 4500s to 6600s, nothing's perfect!

P.S. Citrix, I will respond to your private mail tomorrow!

update

[CODE]
K Weight At 2^ Testing up to 2^ Reserved by
18534 92 1000000 Citrix
23451 230 1250000 2000000 Jean Penne
60849 263 1250000
66741 0 ~~~~~~~~~BASE 4 SIERPINSKI NUMBER~~~~~~~~~

Total Weight = 678
Average Weight= 169.5

Sieving Completed (Billions): 0-3000
[/CODE]

I've completed 60849 up to 1.25 mil with no prime. I'm stopping that one and moving to 64494 to 1.25 mil afterwards I plan to sieve to 5000 billion then we'll see where we're at. as always help any help is appreciated

best of luck all...
Tyler

 Citrix 2006-05-23 05:59

Found something interesting.

[url]http://www.primepuzzles.net/problems/prob_036.htm[/url]

Only 2 even candidates left to find.
(May be we should focus on the 2 odd k's (To 2 Million) we have left, atleast we will be able to acomplish something. As it is, there are only 3 people working on this project. What do you think?)

 Jean Penné 2006-06-05 18:53

Should we focus on odd k's ?

[QUOTE=Citrix]Found something interesting.

[url]http://www.primepuzzles.net/problems/prob_036.htm[/url]

Only 2 even candidates left to find.
(May be we should focus on the 2 odd k's (To 2 Million) we have left, atleast we will be able to acomplish something. As it is, there are only 3 people working on this project. What do you think?)[/QUOTE]

This is interesting, indeed!

For now, my k=23451 is at n=1301228 base two, and I am continuing...
But I cannot presently take the remaining free odd k=60849...
Regards,
Jean

 Citrix 2006-06-21 20:15

[CODE]
K Weight At 2^ Testing up to 2^ Reserved by
18534 92 1000000 Citrix
23451 230 1250000 2000000 Jean Penne
60849 263 1250000
66741 0 ~~~~~~~~~BASE 4 SIERPINSKI NUMBER~~~~~~~~~

Total Weight = 678
Average Weight= 169.5

Sieving Completed (Billions): 0-3000
[/CODE]

I have started working on my k, I am at 1060000. Tyler have you been able to find any more factors, that should reduce some work for me. Anyway, are you sieving till 1.5 M or 2M. Going beyond 1.5 M is alot of work.

[QUOTE=Citrix]I have started working on my k, I am at 1060000. Tyler have you been able to find any more factors, that should reduce some work for me. Anyway, are you sieving till 1.5 M or 2M. Going beyond 1.5 M is alot of work.[/QUOTE]

actaully I haven't been seiving at all...yet...I've still been working on my reservation. yesterday I just passed 1.2 M on my k, when I get home I could probably do some calculations to determine when I'll be done. I can post those tomorrow.

when I do finish I'll sieve on the same files that I have all along. they're the ones for jjsieve, that go up to a max of 2 M for each k. I'll just move them up to where everyone is right now and run them.

lets find a prime!
-Tyler

 Jean Penné 2006-06-28 14:33

Continuing k=23451, taking k=60849

Hi,

For k=23451, I am now at n=1353164 ; no prime, continuing...

I can now also take k=60849 from n=1250000 on an other PC, if you agree.

The date of the presieved file I am using for k=60849 is 09 Dec. 2005, please,
let me know if you have a more recent one...

Regards,
Jean

okay I'm back. there have been internet connectivity issues where I'm staying. I finally finished my reservation on 64494 to 1.25 M, finding no prime.:no: so I am going to proceed as I stated before and resume sieving for a while. Jean I don't believe that the I have done any sieving since the file you have, so you should be able to proceed fine. does anyone have any suggestions for how often I should upload the new files?

let's finally find a new prime~!
-Tyler

 Citrix 2006-07-08 06:03

You can remove the values upto 1325000 for my k. They are being PRPed. Expected date of completion is 20 July. Sieved file around then will be appreciated.

edit:
One interesting thing: All the above k's are 3*prime or 9*prime if you do not count the even factors. What a coincidence, since this thread is under the PSP project.

 jasong 2006-07-14 19:27

I should finish my base-5 PRPing sometime Sunday night. I have a 2.8GHz dual-core Pentium-D that would love to help with this if someone could send me a preprocessed(base-2, all n-values even) file for me to LLR.

 Citrix 2006-07-15 01:40

1 Attachment(s)
[CODE]
K Weight At 2^ Testing up to 2^ Reserved by
18534 92 1060000 1325000 Citrix
23451 230 1353164 2000000 Jean Penne
60849 263 1250000 2000000 Jean Penne
64494 93 1250000
66741 0 ~~~~~~~~~BASE 4 SIERPINSKI NUMBER~~~~~~~~~

Total Weight = 678
Average Weight= 169.5

Sieving Completed (Billions): 0-3000 (In progress upto 5000)

[/code]

Post range you are working on, before starting. So there is no double booking of work.

Thanks for joining the project, attached are the files, sieved to 3T.

edit:- One more thing, is your computer stable? Please run a Prime95 tourture test before starting your range. There is no double check for this project, so all missed primes are missed.

1 Attachment(s)
here's a new file through 3583...sorry had to do it fast wasn't able to remove out what you've completed citrix. or break it into individual files...not many new factors are being found...but every little bit helps. continuing onwards...

 Citrix 2006-07-22 04:33

[QUOTE=tcadigan]here's a new file through 3583...sorry had to do it fast wasn't able to remove out what you've completed citrix. or break it into individual files...not many new factors are being found...but every little bit helps. continuing onwards...[/QUOTE]

Thanks for the sieve file.

I haven't finished till 1.325 yet, it might take 1-2 more weeks, 200 candidates remaining. (I think I miscalculated)

Once I am done till there, I will stop. I will not PRP any more candidates. It just takes too much time from the fast computers I have. I prefer to put them on PSP. Slow computers take very long to do candidates >1M

As for finding too few factors, I suggest you stop the sieve and PRP instead. P-1 may be better for factoring, you might want to run some tests first.

I don't know how fast Jean's computers are and how far he is planning on extending his k's. It might be a good idea to PRP than sieve.

edit

[CODE]
K Weight At 2^ Testing up to 2^ Reserved by
18534 92 1325000
23451 230 1353164 2000000 Jean Penne
60849 263 1250000 2000000 Jean Penne
64494 93 1250000
66741 0 ~~~~~~~~~BASE 4 SIERPINSKI NUMBER~~~~~~~~~

Total Weight = 678
Average Weight= 169.5

Sieving Completed (Billions): 0-3000 (In progress upto 5000)

[/code]

1 Attachment(s)
[CODE]
K Weight At 2^ Testing up to 2^ Reserved by
18534 92 1325000
23451 230 1353164 2000000 Jean Penne
60849 263 1250000 2000000 Jean Penne
64494 93 1250000
66741 0 ~~~~~~~~~BASE 4 SIERPINSKI NUMBER~~~~~~~~~

Total Weight = 678
Average Weight= 169.5

Sieving Completed (Billions): 0-5000

[/code]

I've finally finished my sieving reservation up to 5000 billion, Citrix I think you're right that at this point in time it's probably better to just PRP the candidates. attached is the latest dat and the individual files. if I can get a status update (or rather just a confirmation of completion Citrix) then I can get the files updated to the right point as well. I think they're decently far behind at the moment.

I'm also going to be taking a 1-2 week break starting now since I am moving again. thankfully the new place will have a MUCH better internet connection then here!

best of luck,
-Tyler

 Jean Penné 2006-08-23 14:50

Thanks!

Thank you, Tyler, for the new sieved files! I updated my input files according to them.

For k = 23451, I am now at n = 1430648, no primes, continuing...
(P4 2.53 GHz)

For k = 60849, I am now around n = 1300000, no primes, continuing...
(T2300 1.66 GHz)

I think we have now to be brave while facing this desert crossing...

Best Regards,
Jean

 Citrix 2006-08-23 23:06

k=18534 complete to 1325000
I would like to put a machine on this project, unfortunately all my computers are turned off this summer, so I am waiting for things to cool off, before I can do any serious prime finding.

 Kosmaj 2006-08-24 01:43

Jean Penne et al.

I see that you are very serious in your search, and I wish you every success, an oasis before long, in the form of a nice, big prime! :cool:

 Jean Penné 2006-08-24 18:28

[QUOTE=Kosmaj;85461]I see that you are very serious in your search, and I wish you every success, an oasis before long, in the form of a nice, big prime! :cool:[/QUOTE]

Thanks! Only four k candidates are remaining, but it is possible than one or
more of them would be out of reach for a while... I hope this bad possibility will be disproved soon!

Regards,
Jean

 Mystwalker 2006-08-24 19:10

I just started working on k=64494. I don't know how far I get, as I currently only have a single Pentium-M available. But it should help nevertheless. :smile:

I wonder why there are a lot more candidates for k=64494 left than for k=18534, given they have almost the same weight.

 Citrix 2006-08-25 00:35

The wieghts are screwed up due to a sampling error.

 Mystwalker 2006-09-12 20:44

Status update, reflecting all recent changes:

[CODE]
K Weight At 2^ Testing up to 2^ Reserved by
18534 92 1325000
23451 230 1430648 2000000 Jean Penne
60849 263 1300000 2000000 Jean Penne
64494 93 1253714 1300000 Mystwalker
66741 0 ~~~~~~~~~BASE 4 SIERPINSKI NUMBER~~~~~~~~~

Total Weight = 678
Average Weight= 169.5

Sieving Completed (Billions): 0-5000

[/code]

 Jean Penné 2006-09-13 19:07

To-day status from my present results :

[QUOTE=Mystwalker;87002]Status update, reflecting all recent changes:

[CODE]
K Weight At 2^ Testing up to 2^ Reserved by
18534 92 1325000
23451 230 1430648 2000000 Jean Penne
60849 263 1300000 2000000 Jean Penne
64494 93 1253714 1300000 Mystwalker
66741 0 ~~~~~~~~~BASE 4 SIERPINSKI NUMBER~~~~~~~~~

Total Weight = 678
Average Weight= 169.5

Sieving Completed (Billions): 0-5000

[/code][/QUOTE]

23451 is tested up to n = 1480004, continuing...
60849 is tested up to n = 1320654, continuing...

so, the status becomes :

K Weight At 2^ Testing up to 2^ Reserved by
18534 92 1325000
23451 230 1480004 2000000 Jean Penne
60849 263 1320654 2000000 Jean Penne
64494 93 1253714 1300000 Mystwalker
66741 0 ~~~~~~~~~BASE 4 SIERPINSKI NUMBER~~~~~~~~~

Total Weight = 678
Average Weight= 169.5

Sieving Completed (Billions): 0-5000

Tanks, and best regards,
Jean

 Jean Penné 2006-10-11 16:10

My to-day's status

k = 23451 is tested up to n = 1535192, no primes, continuing...

k = 60849 is tested up to n = 1351206, no primes, continuing...

Regards,
Jean

 Mystwalker 2006-10-15 17:40

Status update, reflecting all recent changes:

[CODE]
K Weight At 2^ Testing up to 2^ Reserved by
18534 92 1325000
23451 230 1535192 2000000 Jean Penne
60849 263 1351206 2000000 Jean Penne
64494 93 1266026
66741 0 ~~~~~~~~~BASE 4 SIERPINSKI NUMBER~~~~~~~~~

Total Weight = 678
Average Weight= 169.5

Sieving Completed (Billions): 0-5000[/code]

Unfortunately, my computer is no working at the moment. Currently, I have no time to fix it, so I unreserve my range for the time being. Maybe I'll continue when everything is working again...

 Mystwalker 2006-10-15 17:45

Btw.:
Does anyone want the residue file?

With Mystwalker bowing out for the time being. I'll step back in and continue from where he left off. As far as I know we're not collecting residues, since there are so few members involved, doublechecking isn't really an option without a serious time investment. we're just going on the hope that we've got stable comps

 Jean Penné 2006-12-04 17:12

My to-day's status

k = 23451 : tested up to n = 1601888

k = 60849 : tested up to n = 1406310

No primes... continuing the desert crossing!

Regards,
Jean

P.S. : I never used any overclocking on my machines, so I have confidence enough in these results... Nevertheless, I am keeping all the residues.

my current status is:

k = 64494: at n = 1362818 no prime...still going on...just keep plugging away:smile:

 geoff 2006-12-07 02:16

I would like to do some sieving, could someone send me the sieve files (g_w_reynolds at yahoo.co.nz) and allocate a range of 500 billion p? Thanks.

[QUOTE=geoff;93475]I would like to do some sieving, could someone send me the sieve files (g_w_reynolds at yahoo.co.nz) and allocate a range of 500 billion p? Thanks.[/QUOTE]

you've got mail. Thanks for the help!

Status Update

[CODE]
K Weight At 2^ Testing up to 2^ Reserved by
18534 92 1325000
23451 230 1601888 2000000 Jean Penne
60849 263 1406310 2000000 Jean Penne
66741 0 ~~~~~~~~~BASE 4 SIERPINSKI NUMBER~~~~~~~~~

Total Weight = 678
Average Weight= 169.5

Sieving Completed (Billions): 0-5000
Sieving Reserved (Billions): 5000-5500
[/code]

 geoff 2006-12-08 02:15

At p=5e12, the sieve speed for a P2/400 running Linux is:

proth_sieve_cmov 0.42: 193 kp/s
sr2sieve-1.4.9-linux32-i686: 340 kp/s

If anyone wants to try out sr2sieve, there are some binaries [url=http://www.geocities.com/g_w_reynolds/sr5sieve/tests/]here[/url].

 Citrix 2006-12-08 05:04

[QUOTE=geoff;93558]At p=5e12, the sieve speed for a P2/400 running Linux is:

proth_sieve_cmov 0.42: 193 kp/s
sr2sieve-1.4.9-linux32-i686: 340 kp/s

If anyone wants to try out sr2sieve, there are some binaries [url=http://www.geocities.com/g_w_reynolds/sr5sieve/tests/]here[/url].[/QUOTE]

That is impressive. Have you tried your program for PSP's dat?

[QUOTE=geoff;93558]At p=5e12, the sieve speed for a P2/400 running Linux is:

proth_sieve_cmov 0.42: 193 kp/s
sr2sieve-1.4.9-linux32-i686: 340 kp/s

If anyone wants to try out sr2sieve, there are some binaries [url=http://www.geocities.com/g_w_reynolds/sr5sieve/tests/]here[/url].[/QUOTE]

ooooo nice!!!
I just ran a quickie....just to see what speed it gives. it's nice big boost^^

at 5500 billion I'm getting 800 kp/s
I don't remember the exact numbers I was getting with jjsieve, but it was something down in the 400-500 range iirc (don't have time to do a full test right now)

this is a 3.2 p4 HT, with a c120 gnfs sieving, and llr for this project picking up the extra cycles. so I would expect that 800 kp/s to jump even higher if I was running just it on my system.

this is awesome because it puts 1000 billion of sieving in reach for 2 weeks +/- a couple days.

great work with your program Geoff! :bow:

 S485122 2006-12-08 08:07

[QUOTE=geoff;93558]If anyone wants to try out sr2sieve, there are some binaries [url=http://www.geocities.com/g_w_reynolds/sr5sieve/tests/]here[/url].[/QUOTE]
The files containing the P4 and prescott versions have some problems with extraction.

I do not have these problems with the 1.4.8 versions...

 Xentar 2006-12-08 08:17

[QUOTE=geoff;93558]sr2sieve-1.4.9-linux32-i686: 340 kp/s
[url=http://www.geocities.com/g_w_reynolds/sr5sieve/tests/]here[/url].[/QUOTE]

Is sr2sieve right? Shouldn´t it be sr4sieve, or something like that?

 thommy 2006-12-08 16:00

[QUOTE=Xentar;93580]Is sr2sieve right? Shouldn´t it be sr4sieve, or something like that?[/QUOTE]

a*4^b+1=a*2^(2*b)+1

and thats the form which is sieved i think

 Xentar 2006-12-08 19:43

[QUOTE=thommy;93605]a*4^b+1=a*2^(2*b)+1

and thats the form which is sieved i think[/QUOTE]

ok, thats possible - didnt think about that, sry.
But then, we would need another input file, because of 2*b, right?

 thommy 2006-12-09 08:40

sure. but thats taken care of.

 geoff 2006-12-10 22:45

[QUOTE=Jacob Visser;93578]The files containing the P4 and prescott versions have some problems with extraction.

I do not have these problems with the 1.4.8 versions...[/QUOTE]
There is some room for confusion here: note that sr2sieve is for base 2 only, sr5sieve is for base 5 only.

File corruption is possible, I use floppy disks to transfer the files before upload :-(

[QUOTE]
Is sr2sieve right? Shouldn´t it be sr4sieve, or something like that?
[/QUOTE]
It might be slightly faster to recompile the program to use base 4 instead, but the files are already in base 2 format so it is probably not worth the effort.

[QUOTE]
That is impressive. Have you tried your program for PSP's dat?
[/QUOTE]
Yes, it is still slower than proth_sieve for PSP. Sr2sieve seems to work better with a small range of n or a large number of k. (But sr2sieve can sieve Sierpinski and Riesel numbers together, so if PSP and Rieselsieve were using the same n range then the difference might be less for a combined sieve).

 Citrix 2006-12-10 23:39

I think once you implement the SPH algorithm, your program should be faster than proth_sieve. Any plans to implement SPH algorithm?

 geoff 2006-12-11 00:02

[QUOTE=Citrix;93780]I think once you implement the SPH algorithm, your program should be faster than proth_sieve. Any plans to implement SPH algorithm?[/QUOTE]

Is this [url=http://www.mersenneforum.org/showpost.php?p=89333&postcount=2]post[/url] a description of the SPH algorithm?

I have been thinking about how to implement those ideas, but I think it is still quite a lot of work, and I may not have a lot of time to work on the program in 2007.

The source code is there if anyone wants to improve it, or to use it as a base for their own program.

 Citrix 2006-12-13 00:34

[QUOTE=geoff;93781]Is this [url=http://www.mersenneforum.org/showpost.php?p=89333&postcount=2]post[/url] a description of the SPH algorithm?
[/QUOTE]

Looks like the SPH algorithm.

new files and status

1 Attachment(s)
[CODE]
K Weight At 2^ Testing up to 2^ Reserved by
18534 92 1325000
23451 230 1601888 2000000 Jean Penne
60849 263 1406310 2000000 Jean Penne
66741 0 ~~~~~~~~~BASE 4 SIERPINSKI NUMBER~~~~~~~~~

Total Weight = 678
Average Weight= 169.5

Sieving Completed (Billions): 0-5500
[/code]

geoff finished his range and found 31 new factors. attached files are each k's file with the numbers removed. thanks!:smile:

if interested the factors found were:
[code]
5005994642413 | 23451*2^1924232+1
5013026869583 | 23451*2^1924988+1
5017001339947 | 23451*2^1661624+1
5019761756783 | 60849*2^1706094+1
5029175730743 | 60849*2^1419090+1
5042363284489 | 60849*2^1385166+1
5057071611461 | 60849*2^1854066+1
5084683863607 | 18534*2^1799454+1
5110582644113 | 23451*2^1788944+1
5123126337383 | 60849*2^1879590+1
5132064179287 | 18534*2^1993014+1
5132383706077 | 60849*2^1442706+1
5138529248959 | 60849*2^1649886+1
5159363407993 | 23451*2^1896992+1
5204363940289 | 23451*2^1836784+1
5213462298949 | 64494*2^1852658+1
5239864808359 | 60849*2^1870674+1
5267254635953 | 23451*2^1618844+1
5278057962883 | 64494*2^1576346+1
5288032742747 | 60849*2^1688310+1
5309811652417 | 60849*2^1414410+1
5314758535139 | 60849*2^1606926+1
5387876951543 | 64494*2^1707554+1
5388081137773 | 23451*2^1976912+1
5407646427083 | 23451*2^1654772+1
5432400900539 | 64494*2^1428266+1
5434314816137 | 60849*2^1481754+1
5483115369931 | 60849*2^1766574+1
5487123017581 | 60849*2^1765746+1
5493702516077 | 60849*2^1598586+1
5499608142031 | 64494*2^1849322+1
[/code]

 Citrix 2007-01-01 20:25

[CODE]
K Weight At 2^ Testing up to 2^ Reserved by
18534 92 1325000 Citrix
23451 230 1601888 2000000 Jean Penne
60849 263 1406310 2000000 Jean Penne
66741 0 ~~~~~~~~~BASE 4 SIERPINSKI NUMBER~~~~~~~~~

Total Weight = 678
Average Weight= 169.5

Sieving Completed (Billions): 0-5500
[/code]

Reserving 18534!

 geoff 2007-01-08 06:47

Reserving 5500-7500 for sieving.

 Citrix 2007-01-23 20:33

18534 is at 1.5M no primes, continuing. Geoff, you might want to update the sieve file for some extra boost.

1 Attachment(s)
[CODE]
K Weight At 2^ Testing up to 2^ Reserved by
18534 92 1500000 Citrix
23451 230 1601888 2000000 Jean Penne
60849 263 1406310 2000000 Jean Penne
66741 0 ~~~~~~~~~BASE 4 SIERPINSKI NUMBER~~~~~~~~~

Total Weight = 678
Average Weight= 169.5

Sieving Completed (Billions): 0-7500
[/code]

Geoff has completed his range and sends "I got about 415 kp/s on a P2/400 with sr2sieve 1.4.18 for this range."

the resulting files are attached

 Mystwalker 2007-01-31 21:44

Can you give me some instructions on how to use sr2sieve and the sieve file for sierpinski base 4?
Then I could do some more sieving.

 Jean Penné 2007-02-01 15:22

How did you compute the weights?

I am wondering at the method you were using to compute the weights of the remaining four candidates...
While using the psieve 3.21 program written by Chris Nash and Paul Jobling :

psieve -q -e -b4 <k value>, I found :

23451 : 460
60849 : 526

so, exactly two times yours!
And the program refuses to compute the weights for 18534 and 64494 because these k values are even...
I am very interested to know about that, because I wish now to estimate the chance we have to prove the base 4 Sierpinski conjecture, using the method suggested by Yves Gallot in his paper :

"On the number of primes in a sequence"

For now, I computed all the "frequencies" as defined by Ray Ballinger and Wilfrid Keller, up to f19, and registered all of the 22242 corresponding Keller primes (k, n) pairs, so, our work can now be precisely described.

(I will communicate these results soon)

I can assert the four remaining candidates belong at least to f20, but it remains to evaluate the chance we have to eliminate all of them in a not too far future!

Thank you by advance and Best regards,
Jean

 geoff 2007-02-01 23:04

[QUOTE=Mystwalker;97426]Can you give me some instructions on how to use sr2sieve and the sieve file for sierpinski base 4?
Then I could do some more sieving.[/QUOTE]

Download sr2sieve from [url]http://www.geocities.com/g_w_reynolds/sr2sieve/[/url]. For example: To sieve from 5500 to 7500 billion, create a new directory containing a copy of SoB.dat (case-sensitive name), and a text file sr2work.txt containing the line "5500,7500" (without quotes). Then run `sr2sieve -s'. You can stop with ctrl-c and it will resume from where it left off when restarted. The factors will be recorded in factors5500.txt.

 Citrix 2007-02-03 00:14

[QUOTE=Jean Penné;97454]I am wondering at the method you were using to compute the weights of the remaining four candidates...
While using the psieve 3.21 program written by Chris Nash and Paul Jobling :

psieve -q -e -b4 <k value>, I found :

23451 : 460
60849 : 526

so, exactly two times yours!
And the program refuses to compute the weights for 18534 and 64494 because these k values are even...
I am very interested to know about that, because I wish now to estimate the chance we have to prove the base 4 Sierpinski conjecture, using the method suggested by Yves Gallot in his paper :

"On the number of primes in a sequence"

For now, I computed all the "frequencies" as defined by Ray Ballinger and Wilfrid Keller, up to f19, and registered all of the 22242 corresponding Keller primes (k, n) pairs, so, our work can now be precisely described.

(I will communicate these results soon)

I can assert the four remaining candidates belong at least to f20, but it remains to evaluate the chance we have to eliminate all of them in a not too far future!

Thank you by advance and Best regards,
Jean[/QUOTE]

I can't remember for sure. I did use psieve. The weights are base 2. So the actual base 4 weights will be twice this.

For the even k's, you calculate this

weight of k/2 in base 2 and base 4. Divide weight in base 4 by 2 and subtract from weight in base 2. TO get actual weight. THen can multiply by 2 to get weight of k in base 4.

What is the status of your k's, so we can update the sieve file.

:smile:

[QUOTE=geoff;97479]Download sr2sieve from [url]http://www.geocities.com/g_w_reynolds/sr2sieve/[/url]. For example: To sieve from 5500 to 7500 billion, create a new directory containing a copy of SoB.dat (case-sensitive name), and a text file sr2work.txt containing the line "5500,7500" (without quotes). Then run `sr2sieve -s'. You can stop with ctrl-c and it will resume from where it left off when restarted. The factors will be recorded in factors5500.txt.[/QUOTE]

Mystwalker...so...just stating the obvious...you'd get the dat for the most recent zip posted...rename it to SoB.dat and then follow the rest of geoff's instructions.

whenever you're done make the results available, I seem to have taken up that since there isn't a whole lot of movement in the project and it's just as easy for me to do it as anyone else

 Citrix 2007-02-03 04:36

[QUOTE=tcadigan;97558]Mystwalker...so...just stating the obvious...you'd get the dat for the most recent zip posted...rename it to SoB.dat and then follow the rest of geoff's instructions.

whenever you're done make the results available, I seem to have taken up that since there isn't a whole lot of movement in the project and it's just as easy for me to do it as anyone else[/QUOTE]

The Sob.dat in the Zip is outdated. You can remove the stuff below 1.5M for my k. Should be give atleast a 10% boost.:smile:

file update

1 Attachment(s)
there updated with the last time Jean reported...and where I'm currently at...and what Citrix has done

dat file dropped for 90 kb to 75 kb

 Jean Penné 2007-02-04 10:36

Excuse me for this late response...

To-day :

k = 23451 is up to 1,677,664 base two, no prime, continuing...

k = 60849 is up to 1,501,350 base two, no prime, continuing...

I also have a first assessment about our chance of proving the base 4 Sierpinski conjecture :

it is about 8.6*10^-5 in the present range (f20, n = 1,048,576 to 2,097,150)

and about 4.5*10^-4 in the next range (f21, n = 2,097,152 to 4,194,302)

but the number of remaining primes to be found is expected to be 8 by this calculus, while it is really 4, so, I think these assessments are pessimistic!

"Que sera sera..."

Jean

 Citrix 2007-02-04 19:26

Some :question:

What are our chances of finding 1 prime in this range. (n<2M)?
If the chances are close to 0, should we stop the work?
Do we need more sieving, does anyone know how long it takes to find a factor?
Should we p-1 instead of sieve?
Should Mystwalker (if willing) PRP instead of sieve/p-1?
Till where will we have to PRP to finish the problem?

Thanks

1 Attachment(s)
since Jean just updated his stats....I'll update the files again.

dat drop from 75 kb to 67 kb

 Jean Penné 2007-02-05 21:38

Our chances to find primes...

I think I can only respond to the 1) and 2) questions by Citrix :

1) For the 4 k values remaining, I can estimate the probability to find a prime in the present n range, and in the next n ranges, starting from the present one :

kvalue : 18534 23451 60849 64494

to 2^21 : 0.08 0.24 0.28 0.20
to 2^22 : 0.16 0.43 0.48 0.36
to 2^23 : 0.23 0.57 0.63 0.49
to 2^24 : 0.29 0.67 0.73 0.59
to 2^25 : 0.35 0.75 0.80 0.67
to 2^26 : 0.40 0.81 0.86 0.74

I could continue, but we are now above the 10 million digits candidates!

2) We have NO reason to be discouraged : These probabilities are not so small, and we are very lucky because of having still only 4 primes to found!
Comparing to SoB project, I see they are already in the 2^23 to 2^24 range, and with still 8 primes to found, the next beeing expected to have 19 millions digits!

Here are the formulas I am using for these estimates :

The expected number of primes found in the range N1 to N2 is :

P(k,N1,N2) = w(k)/2log(2)*log[(2N1+log2(k))/(2N2+log2(k))]

w(k) beeing the weight of k (the weight computed with small n's and small prime divisors, not the Nash-Jobling weight).
This is the formula by Yves Gallot, adapted to base 4 (I did'nt need to translate it, the expected frequencies beeing not too bad when compared to the experimental values).

And the chance to find a prime in the range is 1-exp(-P) admitting a Poisson law...

Good luck for this project, and Best Regards,
Jean

 Jean Penné 2007-02-06 07:28

Erratum on my previous post...

In my previous post, would you read :

The expected number of primes found in the range N1 to N2 is :

P(k,N1,N2) = w(k)/2log(2)*log[(2*N2+log2(k))/(2*N1+log2(k))]

Sorry for the error...

Jean

 Mystwalker 2007-02-06 22:32

Thanks for the sieving instructions, everyone! :smile:
I will start sieving someone this week, depending on when my PSP sieve ranges are complete.

@Citrix:
I think the question sieve vs. PRP should once again be very influenced by the processor architecture. In my case, this will be a Core Duo*, so I'm not sure whoch one is the better technical alternative. But as all k's are currently assigned, I think that, organisatorically, sieving is the better way.

*By the way:
Which of the sr2sieve versions (for Windows) will perform best on this CPU?

 geoff 2007-02-07 02:21

[QUOTE=Mystwalker;97869]In my case, this will be a Core Duo*

*By the way:
Which of the sr2sieve versions (for Windows) will perform best on this CPU?[/QUOTE]
The -pentium4 build probably, lacking a way to compile the -k8 build for Windows.

I am testing some improvements to the sr2sieve code that should make it 20% faster for this project (from 415 kp/s to 500 kp/s on my P2/400). If it works out they will be in version 1.4.20.

 Mystwalker 2007-02-07 22:04

The P4 build is ~1% faster than i686 and ~2% faster than i586 - according to quick benchmarking, probably not enough for such a small deviation.

I could do some sieving, but I'm not sure whether it is efficient for such a small n range (~500K). With the expected probabilities for primes with n<2M, we might discuss increasing the sieving range. But with only 4 k's left, it's of course difficult to find an optimal range...

Btw.:
[CODE]
K Weight At 2^ Testing up to 2^ Reserved by
18534 92 1500000 Citrix
23451 230 1677664 2000000 Jean Penne
60849 263 1501350 2000000 Jean Penne
66741 0 ~~~~~~~~~BASE 4 SIERPINSKI NUMBER~~~~~~~~~

Total Weight = 678
Average Weight= 169.5

Sieving Completed (Billions): 0-7500
[/code]

[QUOTE=Mystwalker;97938]The P4 build is ~1% faster than i686 and ~2% faster than i586 - according to quick benchmarking, probably not enough for such a small deviation.

I could do some sieving, but I'm not sure whether it is efficient for such a small n range (~500K). With the expected probabilities for primes with n<2M, we might discuss increasing the sieving range. But with only 4 k's left, it's of course difficult to find an optimal range...
[/QUOTE]

for my 2 cents....I've thought about bumping to 5 million. I wouldn't be opposed to the 2^23 limit either:wink:

sure the probabilities don't increase a whole lot, but we're starting to get to pretty big numbers if we do find a prime. I agree with you that it might not be worth a whole lot to sieve for the last .5M

I was sieving with JJSieve and went until I was finding factors there as as fast as I was eliminating them with LLR....now with geoff's sieve sieving rates drastically improved (for me). I stick with this project because it's pretty low maintenance and it sucks up the cycles while ggnfs is running concurrently.

 Citrix 2007-02-09 01:24

[QUOTE=tcadigan;97954]for my 2 cents....I've thought about bumping to 5 million. I wouldn't be opposed to the 2^23 limit either:wink:
[/QUOTE]

I don't recommend the idea. It will take alot of computers to reach that goal. With only 4 users working on this project, it will take a long time to finish.

edit: I will be moving to work on k=3^16 once I am done with my range.
Jean, is it possible to speed up the PRP test for 3^16? It is a generalized fermat as well as k*2^n+1? Could a smaller FFT lenght be used?

[QUOTE=Citrix;98045]I don't recommend the idea. It will take alot of computers to reach that goal. With only 4 users working on this project, it will take a long time to finish.[/QUOTE]

as I said I use this project as a extra cycle sink...and every little bit helps...I don't see this as all that pointless of a project and I think users could come someday in the future. we've got fewer than SOB, I don't mind just letting it sit in teh background of my comp and LLR....or sieve....but that's just me:smile:

 Mystwalker 2007-02-12 20:59

Well, I've started NewPGen for k=18534, 1M < n < 2.5M (base 4), as there are the fewest tests left for this k.
I haven't done any work for the other k's so far. But I think we should be ready for a combined sieve effort with sr2sieve once we reach the limit of the current candidate files.

Geoff:
Is there a lower limit for p values in sr2sieve?
So far, I've sieved to p=40M.

 geoff 2007-02-13 03:13

[QUOTE=Mystwalker;98310]Geoff:
Is there a lower limit for p values in sr2sieve?
So far, I've sieved to p=40M.[/QUOTE]
p must be greater than the greatest k value.

 Mystwalker 2007-02-13 18:32

Great (pun not intended)!
So we could prepare the sieving within the next weeks. :smile:

 Jean Penné 2007-03-03 21:25

My to-day status...

k = 23451 is up to n = 1,703,768 base two, no prime, continuing...

k = 60849 is up to n = 1,555,134 base two, no prime, continuing...

Regards,
Jean

 jasong 2007-03-10 21:18

I'm interested in helping this project, just not in the immediate(within the next week or so) future.

Has anyone thought about setting up an LLR server for these numbers? If you did, it would probably be a good idea to set up the numbers as k*[b]2^n[/b]+1 , rather than k*[b]4^n[/b]+1 . Wouldn't want to get errors from people having their computer set up improperly. :)

 thommy 2007-03-11 01:42

[quote=jasong;100478]I'm interested in helping this project, just not in the immediate(within the next week or so) future.

Has anyone thought about setting up an LLR server for these numbers? If you did, it would probably be a good idea to set up the numbers as k*[B]2^n[/B]+1 , rather than k*[B]4^n[/B]+1 . Wouldn't want to get errors from people having their computer set up improperly. :)[/quote]

Not worth it with just 4 ks remaining. And llr handles 4^n as 2^m... that wouldnt be a problem at all. :rolleyes:

 jasong 2007-03-11 21:04

[QUOTE=thommy;100505]Not worth it with just 4 ks remaining. And llr handles 4^n as 2^m... that wouldnt be a problem at all. :rolleyes:[/QUOTE]
If I'm not mistaken(I may be), when the LLR program contacts the server, the only thing transmitted is the k/n pair, not necessarily the b in k*b^n+c.

Am I wrong?

 Jean Penné 2007-03-14 07:28

[QUOTE=jasong;100553]If I'm not mistaken(I may be), when the LLR program contacts the server, the only thing transmitted is the k/n pair, not necessarily the b in k*b^n+c.

Am I wrong?[/QUOTE]

It is not quite exact ; the LLRNET server takes into account the header of the Newpgen file, and sends the info to the client, so, the base info is not lost.

 Jean Penné 2007-04-02 20:10

My to-day's status

k = 23451 is up to n = 1,736,684 base two, no prime, continuing...

k = 60849 is up to n = 1,600,626 base two, no prime, continuing...

Regards,
Jean

 jasong 2007-05-11 20:16

Is this project still active?

[QUOTE=jasong;105826]Is this project still active?[/QUOTE]

yep it's still active, at least as far as I'm concerned....I think Jean and Citrix are in on it too. the general held opinion is that we finish out to 2 mil, then decide from there. at this point in time sieving for such a small amount of remaining isn't worthwhile.

that said recently I had to move (which required me to be out for a week) and I'm currently having HD problems. It's practically dead...I can't run I/O intensive stuff on it (so no ggnfs :cry:). I'm looking at getting a new drive, just haven't been able TO look much recently.

for those interested I'm at:
k=64494 is up to n=1628786 base 2, no prime, pushing on...

 jasong 2007-05-15 00:31

How many k are left?

Never mind there are 4 left?

/me decides to post an update of progress here.

k=64494 is up to n=1628786 base 2, no prime, pushing on...
k = 23451 is up to n = 1,736,684 base two, no prime, continuing...
k = 60849 is up to n = 1,600,626 base two, no prime, continuing...

k=18534 unknown(at least as far up in the posts that I checked)
edit by Citrix: 18534 is done to 1.5M

 jasong 2007-05-15 01:32

Even though nobody asked, I decided that I want to help. ;)

I'm sieving all the k's to 1 billion, and am hoping to get some help in making it one file, to sieve with sr2sieve(or sr4sieve, if someone wants to help me with compiling)

 Citrix 2007-05-15 01:34

[QUOTE=jasong;106099]Even though nobody asked, I decided that I want to help. ;)

I'm sieving all the k's to 1 billion, and am hoping to get some help in making it one file, to sieve with sr2sieve(or sr4sieve, if someone wants to help me with compiling)[/QUOTE]

what nmax value are you using?

[QUOTE=jasong;106099]Even though nobody asked, I decided that I want to help. ;)

I'm sieving all the k's to 1 billion, and am hoping to get some help in making it one file, to sieve with sr2sieve(or sr4sieve, if someone wants to help me with compiling)[/QUOTE]

please take note that we have (a whole lot of it was me in the later stages...) have sieved all k's for nmax = 2 million to 7.5 billion so I hope you aren't sieving any of that again :)

 Jean Penné 2007-05-15 06:35

My present day's status

k=23451 is up to n=1,779,364 base two, no prime, continuing...

k=60849 is up to n=1,659,306 base two, no prime, continuing...

I am very glad to see that more help is going! thank you by advance!

I did also some double-checking using NewPgen and LLR :

k=23451 is double-checked up to n=700,000 (that was my starting point using the presieved files from the project).

and k=60849 is now double-checked up to n=723426, continuing...
(my starting point was n=1,250,000).

If you think it would be useful, I can send you the result files.

Regards,
Jean

 jasong 2007-05-15 17:59

[QUOTE=tcadigan;106107]please take note that we have (a whole lot of it was me in the later stages...) have sieved all k's for nmax = 2 million to 7.5 billion so I hope you aren't sieving any of that again :)[/QUOTE]
I'm sieving n=1 million to 5 million(base 4), which ultimately means all even values for base-2 from 2 to 10 million.(But you guys probably already knew that. Me, I had to start over after about 4 hours because of realizing that little fact.)

 jasong 2007-05-15 18:07

Because of the difficulty of transferring files from my crunching boxes to my main PC, I've been forced to do sieving on my Pentium-D, so if anyone wants to sieve k = 60849 or k=18534 to 1 billion on a fast PC, that would be appreciated.

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